Find the value of '?' if the mean of the data set 18,16,22,13,?=16

Options

A. 9
B. 11
C. 10
D. 12

Answer

To find the value of '?' in the data set 18, 16, 22, 13, ?, given that the mean is 16, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Mean Formula**:
The mean (average) of a data set is calculated by dividing the sum of all observations by the number of observations.

\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

2. **Identify the Given Values**:
- The observations are: 18, 16, 22, 13, and '?'.
- The mean is given as 16.
- The number of observations (n) is 5.

3. **Set Up the Equation**:
Using the mean formula, we can set up the equation:
\[ 16 = \frac{18 + 16 + 22 + 13 + ?}{5} \]

4. **Multiply Both Sides by 5**:
To eliminate the fraction, multiply both sides by 5:
\[ 80 = 18 + 16 + 22 + 13 + ? \]

5. **Calculate the Sum of Known Observations**:
Now, calculate the sum of the known observations:
\[ 18 + 16 = 34 \]
\[ 34 + 22 = 56 \]
\[ 56 + 13 = 69 \]
So, the sum of the known observations is 69.

6. **Substitute Back into the Equation**:
Substitute the sum back into the equation:
\[ 80 = 69 + ? \]

7. **Solve for '?'**:
To find '?', subtract 69 from both sides:
\[ ? = 80 - 69 \]
\[ ? = 11 \]

### Final Answer:
The value of '?' is **11**.

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